Dr. Abner Mallity has some more thoughts on how to control the biplane better.  He believes that it will be possible to produce a well-damped system with quick response using a pitch gyro.  Basically, a pitch gyro is a device that produces a signal proportional to pitch.  (Actually, it's more complex than that because there are dynamics involved in the gyroscope that produce a signal that is more like a second order filtering of the pitch, but that's a more complex model, and it may be one that Mallity cannot yet deal with.)  In any event, the simplest model is one in which the gyro develops a signal exactly proportional to pitch.

        That simple model is included in the block diagram with the simulator below.

Note the following in the system above.

• The pitch signal is multiplied by a variable gain (Call it "a".)
• In the simulator above, you can enter a value for a. Then, you can run the simulation.

• Dr. Mallity needs to know what gain value to choose.  There are two gains to choose, K and a.
• Ultimately you should recommend values for those gains.  Mallity does not trust the simulation.  He wants reasons for why the values should work.
• He needs you to determine whether you can produce a system with small overshoot (less than 10%) with quick response.  (The quicker the better, but at least twice as good as the time response of the original system with K = 0.5.)
• Dr. Mallity believes that you can choose a value for a, and do a root locus for that value of a.
• Determine the root locus for the value of a pre-loaded into the simulator, i.e a = 0.5.
• Explain the time response that you observe for the gain values you choose.  You will need to compare measurements (using the simulation) with values predicted from the root locus for response time (rise time, settling time).